Welcome to the forum!
There are two ways to earn DC quickly:
Breeding and Selling eggs Strategy:
For beginner, if you still don't have Air and Metal Dragon, breeding a Cactus Dragon is a quick and easy way to earn DragonCash (DC) since it can earn you 100,000 DC an hour (breeding and hatching).
Many people also breed an Air Dragon for DC. This is very commonly well known because it only takes four hours to breed and hatch. It sells for 500K so this is a quick and easy way to earn some extra DC. (Note: Fire Dragon breed with Water Dragon makes an Air Dragon.)
Yet this is NOT the best way to earn the most DC in DragonVale.
Breeding Iron Dragon gets you 1,150,000 DC in total of 8 hours. This is so far the most efficient way to earn the most DragonCash so far in DragonVale.
Collecting DC in habitat:
Quake Dragon is the best non-limited dragon money earner for the Earth habitat. (Panlong is best limited dragon money earner in an Earth Habitat)
Bluefire/Frostfire Dragon is the best non-limited dragon money earner for the Cold habitat. (Paper is best limited dragon money earner in an Cold Habitat)
But it's not fun if you just keep breeding and selling.

there are still lots of ways to earn money (winning races, winning colosseum events, collecting party hats on friends park, selling dragons from fails, etc). Play how you want to play it, it's all about fun.